Method and apparatus for phase-encoded homogenized Fourier transform holographic data storage and recovery

ABSTRACT

An apparatus for writing and reading holograms, comprising a spatial light modulator (SLM) operable in phase mode, having a plurality of pixels for generating an object beam that overlaps with a reference beam; a holographic recording medium (HRM) in the path of the object beam; and a first lens element disposed in the path of the object beam between the SLM and the HRM; wherein the HRM is disposed at or near the Fourier transform plane of the first lens element.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/962,202, now U.S. Pat. No. 7,411,708, filed Oct. 8, 2004, whichclaims the benefit of U.S. Provisional Application No. 60/532,795, filedon Dec. 24, 2003 and U.S. Provisional Application No. 60/509,983, filedon Oct. 8, 2003. The entire teachings of the above applications areincorporated herein by reference.

BACKGROUND OF THE INVENTION

One important potential use of volume holograms is in digital datastorage. The three dimensional nature of a volume hologram, which refersto the storage of each bit as a hologram extending throughout the entirevolume of the recording medium, renders volume holograms suitable foruse in high capacity digital data storage. A group of bits can beencoded and decoded together as a two dimensional array of bits referredto as a page.

In Holographic Data Storage (HDS) systems the optics configuration usedfor recording and reading typically comprises a Fourier Transform (FT)geometry that uses a 4f optical imaging system which for recordingincludes a spatial light modulator (SLM) or other optical encodingdevice that displays information.

Mutually coherent object and reference beams form an interferencepattern in the volume of their overlap. A hologram is recorded whenlight-induced changes in the volume of their overlap in the storagemedium, such as photopolymerization, produce a record of the resultinginterference pattern. The essential elements and arrangement of the 4foptical design for recording holograms are: an SLM that encodes theobject beam, a lens element L1, having an effective focal distance f1and which is located at a distance f1 from the SLM in the optical pathof the encoded object beam, for relaying a 2-D Fourier transform of thespatial pattern of the encoded object beam to a plane that is one focaldistance from the lens and a holographic recording medium (HRM), locatedat a distance f1 from the lens element L1 in the optical path of theencoded object beam relayed by the lens element L1.

Reconstruction of a hologram is accomplished by firstly illuminating thehologram with a reference beam that is substantially the same as thereference beam used for recording the hologram, and secondly imaging theresultant diffracted light (reconstructed object beam) onto the detectorarray with a second lens element of the said. 4f optical design. Thefollowing elements are used for reading a reconstructed hologram: a lenselement L2 for relaying an object beam reconstructed by directing areference beam at a storage location in the HRM, having an effectivefocal distance f2 and which is located at a distance f2 from the HRM inthe optical path of a reconstructed object beam; and a light detector,located at a distance f2 from the lens element L2 in the optical path ofthe reconstructed object beam directed by lens element L2. In theaforementioned 4f optical design f1=f2, but in other opticalconfigurations it may be advantageous for f2>f1 and thereby improve SNRof the reconstructed holograms by use of an optical relay system.Additionally, when magnification or demangnification is preferred in theoptical configuration then f2 is not equal to f1.

Typically, an SLM operates in an amplitude mode, whereby the date pageappears as a two-dimensional array of dark and bright pixels. When theFourier transform (FT) of such an amplitude-modulated data page isobtained using a lens element L1, a strong high intensity direct current(DC) spike, that corresponds to the 0^(th) order diffraction, appears atthe center of the Fourier transform at the Fourier plane (focal plane)due to the constructive interference of the light from the SLM pixels inthe bright state. When large numbers of holograms are multiplexed in themedium, co-locationally or substantially overlapped, this intense DCpeak will quickly saturate the dynamic range of a recording material(i.e. deplete the available photopolymerizable component), preventingthe efficient use of the medium, and, additionally, will result insignificant non-uniformity in the modulation depth of the recording forspatial frequencies of the interference pattern of the holographicrecording corresponding to the DC and “alternative current” (AC)components of the FT, and thereby cause poor fidelity in thereconstructed data pages. The intense DC peak at the center and thetypically large amplitude distribution in the AC components of the FTspectrum can also result in nonlinear grating formation, increasing thenoise level in the reconstructed data page.

SUMMARY OF THE INVENTION

The instant invention relates to methods and apparati that can be usedfor recording and retrieving phase-encoded Fourier transform andfractional Fourier transform holograms.

In one embodiment, the present invention is an apparatus for writing andreading holograms comprising a spatial light modulator (SLM) operable inphase mode, having a plurality of pixels, each for generating an objectbeam that overlaps with a reference beam; a holographic recording medium(HRM) in the path of the object beam; and a first lens element disposedin the path of the object beam between the SLM and the HRM. The HRM isdisposed at or near the Fourier transform plane of the first lenselement.

In another embodiment, the present invention is a method of recording ahomogenized hologram, comprising illuminating a spatial light modulator(SLM) operable in phase mode, said SLM having a plurality of pixels,each pixel of the SLM being in either a first state or a second state;controllably changing the state of selected pixels of the SLM, therebychanging the polarization of a light wavefront reflected from ortransmitted through each pixel of the SLM, thereby forming an outputbeam; directing the output beam at a polarization filter, therebychanging the phase of a light wavefront reflected from or transmittedthrough each pixel of the SLM by φ, depending on the state of the pixel,and thereby producing a phase encoded object beam; directing the phaseencoded object beam through a first lens element disposed in the path ofthe object beam between the SLM and a holographic recording medium(HRM), wherein the HRM is disposed at or near the Fourier transformplane of the first lens element; and directing a reference beam at theHRM so as to overlap the reference beam and the phase encoded objectbeam at a selected storage location in the HRM, thereby producing aninterference pattern at the HRM and recording a hologram.

In another embodiment, the present invention is a method of reading aphase-encoded holograms comprising directing a reference beam at alocation in a holographic recording medium where a phase-encoded Fouriertransform hologram or fractional Fourier transform hologram wasrecorded, thereby reconstructing said phase-encoded hologram, saidreconstructed hologram comprising images of edges of pixels, said imagescorresponding to transitions between pixels recorded by light wavefrontshaving different phases; detecting the reconstructed hologram by adetector having resolution sufficient to detect the edges of pixels; andassigning a value of “0” or “1” to each pixel based on the images of theedges of pixels, said images corresponding to transitions between pixelsrecorded by light wavefronts having different phases.

In another embodiment, the present invention is a method of readingholograms, comprising directing a reference beam at a selected locationin a holographic recording medium where a phase-encoded Fouriertransform hologram or fractional Fourier transform hologram wasrecorded, reconstructing a first object beam and directing the firstobject beam to a detector; illuminating a phase spatial light modulator(SLM) displaying a uniform data page, thereby forming a second objectbeam and directing the second object beam to said detector, therebyproducing an interference pattern between the first object beam and thesecond object beam at the detector that reproduces anamplitude-modulated data page; and detecting the amplitude-modulateddata page.

In another embodiment, the present invention is a method of recording ahomogenized hologram, comprising recording a uniform data page hologram;and recording a Fourier transform hologram or a fractional Fouriertransform hologram at the same storage location.

In another embodiment, the present invention is a method of reading ahomogenized hologram, comprising directing a reference beam at aselected location in a holographic recording medium where a phasemodulated Fourier transform hologram or fractional Fourier transformhologram and a uniform phase-encoded data page hologram were recordedusing the same reference beam, thereby reconstructing a first objectbeam, used to record a first homogenized hologram, and a second objectbeam, used to record the uniform data page hologram, thereby producingan interference pattern between the first and second object beams thatreproduces an amplitude-modulated data page; and detecting theamplitude-modulated data page with a light detector.

In another embodiment, the present invention is a method of reading ahomogenized hologram, comprising directing a first reference beam at aselected location in a holographic recording medium where aphase-encoded Fourier transform hologram or fractional Fourier transformhologram and a uniform phase-encoded data page hologram were recordedusing the first and a second reference beams, thereby reconstructing afirst object beam used to record a first phase-encoded Fourier transformhologram or fractional Fourier transform hologram; directing the secondreference beam at the selected storage location in the holographicrecording medium, thereby reconstructing a second object beam used torecord the uniform data page, thereby producing an interference patternbetween the first and second object beams that reproduces anamplitude-modulated data page; and detecting the saidamplitude-modulated data page with a light detector.

In another embodiment, the present invention is a method of searching aholographic recording medium for a specified content, comprisingilluminating a spatial light modulator (SLM) displaying at least onesearch pattern corresponding to a selected content, thereby forming asearch beam; directing the search beam to one or more storage locationson a holographic recording medium where at least one phase-encodedFourier transform hologram or fractional Fourier transform hologram isrecorded, thereby producing at least one reconstructed reference beamwhen the one or more storage locations contain at least onephase-encoded Fourier transform hologram or fractional Fourier transformhologram that contains selected content of the search pattern; anddetecting the at least one said reconstructed reference beam with one ormore light detectors.

In another embodiment, the present invention is a method of recordingmultiplexed holograms, comprising recording a first phase-encodedFourier Transform hologram or a fractional FT hologram with a firstreference beam; and recording a second phase-encoded Fourier Transformhologram or a fractional FT hologram with a second reference beam at thesame location or at a substantially overlapped location on a holographicrecording medium, wherein the angle between the first and the secondreference beams is less than the angular separation between the primarydiffraction peak and the first null of the Bragg angle selectivity curveof the first or the second holograms.

In another embodiment, the present invention is a method of recordingmultiplexed holograms, comprising recording a first phase-encodedFourier Transform hologram or a fractional FT hologram with a firstwavelength; and recording a second phase-encoded Fourier Transformhologram or a fractional FT hologram with a second wavelength at thesame location or at a substantially overlapped location on a holographicrecording medium, wherein the difference between the first and thesecond wavelengths is less than the wavelength separation between theprimary diffraction peak and the first null of the Bragg wavelengthselectivity curve of the first or the second holograms.

The instant invention is particularly useful for holographic datastorage applications where the areal density of stored informationexceeds about 16 Gbits/inch² and where use of content addressable memoryis desirable. The invention can substantially increase the usable datadensity that can be stored in holographic media, such as relatively thinphotopolymers, by firstly providing for recording with uniformmodulation depth at the Fourier transform plane which improves thefidelity and efficiency of the recording and diminishes the requirementsfor laser power during recording, and, secondly, by providing formultiplexed holograms so that the angle, shift and/or wavelengthincrement between holograms is smaller than the corresponding incrementof angle, shift or wavelength between the primary diffraction peak andfirst null of the Bragg selectivity of the multiplexed holograms. Theinvention substantially decreases cross-correlation in contentaddressable searching, and also increases the correlation signalstrength that is obtained from content addressable searches when a smallstored sub-image is to be identified and located within a larger storedimage.

The present invention makes it possible for a full page or partial pagecontent addressable searching to be performed directly on hologramsrecorded with data pages displayed in either amplitude or phase mode.The search method of the instant invention is substantially independentof the fidelity of the holographically recorded information. Anotheradvantage of searching for data using a phase SLM is that it facilitatessearching the holograms without causing cross-correlation that typicallydegrades the signal-to-nosie (SNR) of the search results and therebyimproves discrimination of the search.

Another embodiment of the present invention facilitates edge enhancedreconstruction of the phase data pages recorded as holograms, byproviding for detection of said edge enhanced features of thereconstructed phase data pages and/or providing for assignment of saidfeatures to, by way of example, binary “1” and “0” values, so as toreconstruct the original amplitude data page information.

In still another embodiment the present invention provides forreconstruction of the original data recorded as multiplexed phase datapage holograms by implementing holographic interferometry during theread out process of said holograms.

A further advantage of the method and apparatus of the present inventionis the ability to multiplex recorded holograms and search such hologramsfor content, in a manner such that the areal density of theholographically recorded information can be increased substantially ascompared to conventional methods. This results in substantially highercapacity, higher data transfer rates, and higher speed data search.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 shows a 4f optical system suitable for use in the presentinvention.

FIG. 2 shows an alternative embodiment of a 4f optical system suitablefor use in the present invention.

FIG. 3 shows an optical scheme used to record image plane holograms.

FIG. 4 shows an optical scheme used to record a fractional Fouriertransform hologram.

FIG. 5 is a schematic diagram of an amplitude mode of SLM operation.

FIG. 6 is a schematic diagram of a phase mode of SLM operation.

FIG. 7( a) shows a representative amplitude modulated data page.

FIG. 7( b) shows MATLAB simulation results of a Fourier transform of thedata page shown in FIG. 7( a).

FIG. 7( c) shows MATLAB simulation results of Fourier transform of thedata page in 0 and π phase mode.

FIG. 8 is a schematic representation of a data recovery process thatuses interferometry.

FIGS. 9( a) through 9(c) show experimental results of DC-removed Fouriertransform (FT) of a data page. FIG. 9( a) shows data page. FIG. 9( b)shows an FT (magnified) of amplitude data page. FIG. 9( c) shows FT(magnified) of phase data page, showing reduced DC peak.

FIGS. 10( a) and 10(b) show experimental results of edge detectionmethod. FIG. 10( a) shows holographic edge reconstruction of 4×4 pixeldata page. FIG. 10( b) shows holographic edge reconstruction of 8×8pixel data page.

FIGS. 11( a) through (d) show experimental results of interferometricrecovery of data page. FIG. 11( a) shows direct amplitude image (SLM inamplitude mode). FIG. 11( b) shows data recovered through real-timeinterferometry. FIG. 11( c) shows phase data page (SLM in phase mode),concentric circular rings and darkened annular region near periphery ofimage caused by interference effects associated with the cover glass ofCMOS sensor. FIG. 11( d) shows data recovered through double-exposureinterferometry.

FIGS. 12( a) through (f) show the Results of “content addressed” searchfor holographic recording of thirty (30) binary data pages with an SLMoperated in either phase mode during recording as shown in FIG. 12( a)or amplitude mode as shown in FIGS. 12( b) and (c)-(f). FIG. 12( a)shows search result for blank page with SLM operating in phase mode;FIG. 12( b) shows search result for 15^(th) data page with SLM operatingin amplitude mode for displaying data page search pattern, showingsubstantial cross correlations; FIGS. 12( c)-(f) Search result for15^(th) data page with SLM operating in phase mode for displaying searchpattern for 100%, 75%, 50% and 25% of the content area of the 15^(th)data page, respectively, showing near to zero cross correlations.

FIG. 13 is a representative angular or wavelength selectivity curve of arecorded hologram.

DETAILED DESCRIPTION OF THE INVENTION

A description of preferred embodiments of the invention follows.

The disclosed invention is an apparatus for holographic data storage(HDS) systems that comprises moderately to high numeric aperturecomponents, such as one or more lenses and/or one or more mirrors, and aspatial light modulator (SLM) that is operable to be used in phase modefor the signal beam, said system operable to achieve moderate to highareal density of stored information, and said stored informationcomprising multiplexed holograms. The apparatus and method of thisinvention operates to achieve high areal density, defined as greaterthan about 25 bits/μm², with acceptable SNR, defined as SNRcorresponding to a raw bit-error-rate (BER) of ≦10E-2, for storedinformation that comprises multiplexed holograms, and where acceptableSNR for information that is stored so as to be searchable corresponds toa BER can be >10E-2. A spatial light modulator operable in 0 and π phasemodes, or alternatively in other phase modes, is optionally providedduring recording to substantially remove the dc peak from the Fouriertransform (FT) at the recording plane (i.e. a plane where theholographic recording medium is disposed), thereby providing forhomogenizing the amplitude distribution in said Fourier transformspectrum. A spatial light modulator operable in 0 and π phase modes, oralternatively in other phase modes, is additionally provided so the HDSsystem can perform full or partial content addressable searching, andthe acceptable raw BER of the holographically stored data for theapparatus and method of this invention can be greater than 10E-2 forsaid searching method.

FIG. 1 shows a 4f system suitable for using in the present invention.The signal beam 102, generated by a source 103 and beam shaping optics(BSO), passes through a spatial light modulator (SLM) 104, having aplurality of pixels 106, arranged in a two dimensional array. SLM 104operates to encode signal beam 102 with data information that is to berecorded. SLM 104 can be operable in either an amplitude mode or a phasemode, as will be explained below in greater detail. Generally, SLMs canoperate by transmission, as SLM 104 shown in FIG. 1, or by reflection,as shown in FIG. 2 for SLM 204. Referring to FIG. 1, plane 107 of SLM104 is located at one focal length, f₁, from a first Fourier transformlens element 108, said lens having a large enough diameter (clearaperture) to accept the field of the light that diffracts or reflectsfrom the SLM 104.

As used herein, the term “lens element” refers to one or more elementshaving optical power, such as lenses, that alone or in combinationoperate to modify an incident beam of light by changing the curvature ofthe wavefront of the incident beam of light. Lens element 108, forexample, can comprise more than one lens.

In the 4f optical arrangement shown in FIG. 1, first Fourier transformlens element 108 operates to relay a 2-D Fourier transform of thespatial pattern of the SLM-encoded signal beam 110 to plane 112 (Fouriertransform or focal plane) that is one focal distance f1 away from lenselement 108 and, additionally, is two focal distances (2f1) from SLM104. Holographic recording material 114 can be located at or near plane112.

A second Fourier transform lens element 116, having effective focallength f2, is positioned at a distance f2 from plane 112. In oneembodiment, f2 can be equal to f1. Lens element L2 operates to perform asecond Fourier transform, causing an inverted image of the spatialpattern of SLM 104 to appear at plane 118, which is one focal distancef2 behind second lens element 116. When reference beam 120 a or 120 bimpinges upon the recorded hologram at an incident angle that was usedto carry out recording of a hologram(s), then the light diffracted fromthe hologram(s) forms reconstructed optical beam 122, which passes intosecond lens element 116, is relayed to plane 118. In the embodimentwhere f1 is equal to f2, plane 118 is thus four focal distances f1 awayfrom SLM 104. Plane 118 corresponds to the correlation plane at thedetector array (light detector) 124. Light detector 124 has a pluralityof pixels 126 that can be of the same or of different linear dimensions(x′,y′) as dimensions (x, y) of pixels 106 of SLM 104.

Three types of hologram recording methods are distinguished based on thepositioning of the recording media. In Fourier transform holograms,shown in FIG. 1, the media is placed at the focal plane (plane 112) of alens element disposed in the path of the object beam encoded by an SLM.The other two types are image plane holograms and Fresnel zone holograms(also referred to as fractional FT holograms). Shown in FIG. 3, imageplane holograms are recorded when SLM 302 is the first element in a 4foptical configuration which uses lens elements 304 and 306 to image adata page displayed on SLM 302 to holographic recording medium 308,which is the last element in the configuration. The third type of aholographic recording method, Fresnel zone or fractional FT planeholograms are shown in FIG. 4. In this scheme, holographic recordingmedium 414 is offset from Fourier transform plane 412 by a distance l.While any of the described methods can be used to record a hologramaccording to using methods and apparati of the present invention, thefractional FT method is preferred.

Principles of operation of SLM devices operable in amplitude mode and inphase mode will now be explained with references to FIG. 5 and FIG. 6,respectively.

A device referred herein as “spatial light modulator (SLM)” comprises aplurality of pixels onto which a light beam impinges and either reflectsfrom the SLM (reflection-type SLM) or is transmits through the SLM(transmittal type SLM). (SLM 104 depicted in FIG. 1 is atransmittal-type SLM. FIG. 2 shows a reflection-type SLM 204.) SLMscontemplated can, by way of example, be one of the following: a nematicliquid crystal SLM, a twisted nematic liquid crytal SLM, a ferroelectricliquid crystal SLM, a cholesteric SLM, an SLM that uses arrays ofphotoelastic crystals for polarization modulation, an SLM that usescontrollable micro gratings such as Silicon Light Machines Grating LightValve (GLV) technology or a device that uses a means to dynamicallycontrol refractive or optical path length.

An example of an SLM suitable for use in the present invention is aferroelectric liquid crystal (FLC) SLM, such as Lightcaster™ (1280×768pixels) produced by Displaytech, Inc. The description of FIGS. 5 and 6use an FLC SLM as a non-limiting example. One skilled in the art ofholography will be readily able to adopt any other type of an SLM devicefor the purposes of the instant invention.

Amplitude mode of operation is schematically depicted in FIG. 5.Coherent beam 502, produced by source 504 is passed through a linearpolarizer 506 resulting in input beam 508 having polarization 510 (here,vertical). Each pixel 512 of the FLC SLM can have one of the two statesof its constituent liquid crystals that orient said crystals 45 degreesapart, thereby forming FLC axes 514 a and 514 b, oriented at 45° angle.Even though both axes 514 a and 514 b are shown in FIG. 5, it should beunderstood that each pixel 512 can have its crystals oriented to formeither axis 514 a or axis 514 b, but not both. Controllably applyingvoltage to each pixel changes its optical polarization properties byswitching between liquid crystal states and thus FLC axes 514 a and 514b.

As used herein, the term “optical polarization properties” refers to theability of a material to change the direction of polarization of thelight wavefront impinging onto such material and either reflected ortransmitted through such material.

The SLM is positioned so that one of the two axes, here axis 514 a, isoriented in a direction parallel to the direction of linear polarization510 of the input beam 508. Upon being transmitted through, as shown inFIG. 5, or reflected from pixel 512, the direction of linearpolarization 510 of the input beam 508 is rotated by twice the anglebetween the polarization axis and FLC axes 514 a or 514 b. In theexample shown in FIGS. 5 and 6, the FLC SLM is a reflection type SLM.Accordingly, when input beam 508 is reflected from pixel 512, eitheroutput beam 516 a, having linear polarization 518 a (vertical), oroutput beam 516 b, having linear polarization 518 b (horizontal), isproduced, depending on the state of each pixel 512. Thus rotation ofpolarization 510 is 0° when pixel 512 is in the state having axis 514 aand 90° when pixel 512 is in the state having axis 514 b.

Output beams 516 a or 516 b are then directed through linear polarizer520, which transmits only the light from the pixels whose that haspolarization direction coincided with that of linear polarizer 520. Inthe embodiment, where a reflection-type SLM is used, linear polarizer520 and linear polarizer 506 can be one and the same. As a result, theobserver sees either black (0) or illuminated (1) pixels depending ontheir state of polarization of each pixel.

The amplitude encoding scheme described above is a binary amplitudescheme. Other schemes can be used with the methods of the instantinvention that use a “grey scale” of amplitude, whereby the amplitudedetected by the light detected can vary continuously between zero andthe amplitude of input beam 508.

Phase mode of operation of an SLM device is shown in FIG. 6.

Coherent beam 602, produced by source 604 is passed through linearpolarizer 606 resulting in input beam 608 having polarization direction610 (here, vertical).

The SLM is positioned so that one of the two axes, here axis 614 a, isoriented at an angle −22.5° to the direction of linear polarization 610of the input beam 608. Upon being reflected from pixel 612, as shown inFIG. 6, direction of linear polarization 610 of input beam 608 isrotated by twice the angle between the polarization axis and FLC axes614 a or 614 b. Accordingly, when input beam 608 is reflected from pixel612, either output beam 616 a, having linear polarization 618 a, oroutput beam 616 b, having linear polarization 618 b, is produced,depending on the state of each pixel 612.

Output beams 616 a or 616 b are then directed through polarizing element620, which can be a polarizing beam splitter or a waveplate and therebyselects a polarization direction. Polarizing element 620, which, in theexample of FIG. 6, is a polarizing beam splitter, transmits thep-polarized light (here, horizontally oriented) and reflects thes-polarized light (here vertically oriented). As a result, the observerafter polarizing element 620 sees either the light having a phase ofφ₀=0 (reflected light from 620) or the light having the phase φ₁(transmitted light from polarizing element 620) that is different fromφ₀=0 by +/−π/2, depending on the state of each pixel, and thus the phasedifference between light reflected from pixel 612 for the two states isπ for the light reflected by polarizing element 620.

The scheme described above refers to a phase encoding where a pair ofphases (0, π) are used. Other schemes can be employed, using pairs (0,φ=2π×n/m), where n is a whole number or zero and m is a natural number.

In general, a binary data page used for holographic storage will besimilar to a binary random image, due to the various modulation codesused while creating such a data page. When such a modulation codedbinary digital data page with equal number of 0s and 1s is displayed onthe phase SLM, and when its Fourier transform is, for example, obtainedby a lens, destructive interference of fields at the dc region, from the0 and π pixels or other phase modes of the SLM leads to a Fourierspectrum with no dc peak.

FIG. 7( a) shows a representative amplitude modulated data page. FIG. 7(b) shows MATLAB simulation results of a Fourier transform of the datapage shown in FIG. 7( a). As seen in FIG. 7( c), the dc peak can befully removed by using (0, π) phase mode for representing binary datapages. Consequently, at the FT plane there is a substantiallyhomogenized Fourier spectrum without the presence of the high intensitydc peak.

As used herein, the term “homogenized hologram” refers to a hologramrecorded with a phase-modulated (encoded) object beam resulting insubstantial removal of the DC peak from the Fourier transform at therecording plane that is at or near the Fourier transform plane, andhence homogenizing the amplitude distribution in said Fourier transformspectrum. In a preferred embodiment, a data page to be holographicallyrecorded contains equal number of transparent or opaque pixels (whendisplayed by an SLM operating in amplitude mode) or equal number ofpixels in each polarization state (when displayed by an SLM operating inphase mode).

However, when the data page is recorded with the SLM operable in thephase mode, the reconstructed data cannot be recovered directly by thestandard application of the second Fourier transform to provide forimaging of the hologram diffraction onto the CCD or CMOS detector.

One embodiment of the present invention for recovery of data is hereinreferred to as the method of “edge detection”. Conventionally, duringthe reconstruction of a hologram, the object beam arm is blocked and thehologram(s) is illuminated by the reference beam that was used to recordthe hologram. In one embodiment of the method and apparatus of thisinvention the hologram is read out by use of the reference beam in theconventional manner, with the object arm blocked. This methodreconstructs the phase data page. However, since the dc peak was absentat the FT plane, holographic recording has occurred only for the accomponents of the FT, and, consequently, said reconstruction providesonly an “edge enhanced” reconstruction of the data page corresponding tothe ac frequency components, as shown in FIGS. 10( a) and 10(b) for twolevels of oversampling (SLM pixel size for data page is larger thandetector pixel size), 4×4 and 8×8, respectively, which corresponds totransitions between pixels with difference phases. In one embodiment,the method and apparatus of this invention provides for recovery of databy use of a high-resolution detector that obtains the data from saidedge enhanced image by identification of said transitions. Various meansof identification of said transitions so as to recover the data arecontemplated by the present invention. By way of example, a means ofidentification of said transitions can be assignment of the detectedsignal, located at the periphery of pixels, to a binary value of either0 or 1 for the pixel. It is preferable to use over sampling inreconstruction and detection of the phase data pages, such that x/1 andy/1 pixels in the detector, where x and y are integers equal to two orgreater, correspond to each pixel in the field of said optical encodingdevice, so as to provide for improved differentiation of said phasetransitions. In cases where over sampling is not used, or in cases wherethe fill factor of the detector pixels is less than 100%, such as forhigh resolution detectors, then it is alternatively preferable to shiftthe detector by an amount, such as ½ of a pixel dimension in x or ydirections, so as to provide for improved differentiation of said phasetransitions. One experienced in the art will be able to choose theoptimum shift amount for a particular detector. In an alternativeembodiment the method and apparatus of this invention provides fordetection of said edge-enhanced image and, additionally, for use ofimage processing for detection and analysis of edges and or lines, suchas can perform edge extraction and/or edge contouring of digital images,which, by way of example, can be implemented using software availablefrom Adobe Systems, Inc. or ArcSoft, Inc. or from vendors of machinevision software such as Cognex Corporation or Adept Technology, Inc., orother suitable image capture and analysis software that can performanalysis of the edge enhanced image by use of methods, that by way ofexample, can perform gradient edge enhanced detection preferably on apixel level. In one embodiment of this method one or more fiducialmarkings, or otherwise known marking or pattern, recorded in the phasedata page are used to determine a reference position for a “1” or “0”edge delineation in said reconstruction of the phase data page, andevery other transition of phase change in the page is thereby assignedto the corresponding “1” or “0” binary value to provide forreconstruction of the original amplitude data page.

Various multiplexing methods, such as angular (planar angle orout-of-plane angle), spatioangular, azimuthal, shift (shift in-plane orshift out-of-plane), wavelength, phase-code, speckle, and relatedmethods, as well as combinations thereof, are used to store multiplepages co-locationally within the same volume or in partially overlappingvolumes.

Another embodiment of the present invention for recovery of data isherein referred to as the method of Real-time holographicinterferometry. The invention further provides for reconstruction of theoriginal data recorded as multiplexed holograms by providing forholographic interferometry during the read out process. In oneembodiment of the method of Real-time holographic interferometry of thepresent invention, the object beam is kept ‘ON’ during the illuminationof the hologram by the reference beam during reconstruction of thestored data from a predetermined storage location. In this manner, therecorded object beam is reconstructed by the reference beam, saidreconstruction containing a wavefront corresponding, by way of example,to the distribution of 0 and π pixels or other phase modes of theoptical encoding device used during recording. Concurrently, on thephase SLM or said optical encoding device, a uniform page (i.e. forexample, all pixels in 0 phase mode or π phase mode or other phasemodes) is displayed and propagated to the stored data at thepredetermined storage location. The new object beam from the phase SLMor said optical encoding device, which in a preferred embodiment isadjusted such that the intensity of this object beam is substantiallyequal to the intensity of the holographically reconstructed object beamobtained from illumination with the Reference beam, operates to form aninterference pattern with the holographically reconstructed object beamat the common image plane on the CCD or CMOS detector. In this mannerthe reconstructed intensity pattern from the said interferometric methodproduces an image that corresponds to the original amplitude data pagenotwithstanding effects such as due to the bit error rate of the image.FIG. 8 depicts, by way of example, that 0 and 0 phase pixels produceconstructive interference (binary 1) and 0 and π pixels producedestructive interference (binary 0). This embodiment of the presentinvention further produces better contrast in the recovered data page,because constructive interference gives 4 times the intensity.

Another embodiment of the present invention for recording and recoveryof data is herein referred to as the method of Double exposureholographic interferometry. In this embodiment recording of a blank datapage (i.e. full field super pixel), in addition to the recording of thephase data page, is carried out at or near the FT plane for eachReference beam condition used to multiplex holograms recordedco-locationally or substantially overlapped. When recording a blank datapage, that is paired with a phase data page for each reference beamcondition, it is preferable during recording of the blank data page toattenuate the dc component of the FT of the object beam such that itsintensity is about equal to the intensity of the reference beam[I_(obj)(DC)/I_(ref)]˜1 used during recording of the blank data page.Upon reconstruction with a selected Reference beam condition, thepresence of the blank page hologram in combination with the phase pagehologram provides for an interference of the two resultant diffractionwavefronts thereby providing for reconstruction of the originalamplitude data page. It is preferable that the diffraction efficiency ofeach of the blank data page holograms would be substantially identicalto that of each of the respective data page phase holograms that each issuperimposed with, and, consequently, this method would preferably usean optimized recording schedule.

Still another embodiment of the present invention for recording andrecovery of data is herein referred to as the method of Double referencebeam interferometry. In said embodiment recording of a blank data page(i.e. full field super pixel) with a unique Reference beam condition iscarried out at or near the FT plane, preferably with use of anattenuation of the dc component of the FT, as mentioned above, such thatthe ratio of I_(obj)(DC)/I_(ref)˜1. The presence of this blank hologramamong the overlapped mulitiplexed holograms provides for a diffractionwavefront, upon reconstruction with the correct reference beam, whichcan further provide for creating an interference pattern with thediffraction wavefronts from all of the other phase data pages. Thisembodiment thus requires use of two Reference beam conditionsconcurrently: one for the aforementioned blank page, and one for theselected phase data page that is to be reconstructed. Overlap of the twodiffraction patterns so as to be substantially identical to when theywere recorded is a required condition, so as to reconstruct theamplitude representation of the selected data page. The intensity of thereference beam for reconstruction of the blank data page can be adjustedrelative to that of the reference beam used to reconstruct each of thedata page phase holograms such that the diffracted intensities aresubstantially the same. The two reference beams at the time of readoutneed preferably to be in phase (0 or multiples of 2π) as the diffractedbeams of each travel in the same direction, and this, if needed, can beadjusted at the reconstruction events.

Other embodiments of the method and apparatus of this invention forrecording and recovery of data are contemplated and as such the extentof the invention is not limited to the specifics described herein. Byway of example, use of a shear plate that operates to provide aninterference condition at a defined angle between a recovered wavefrontand a sheared wavefront can provide for reconstruction of an amplitudeimage from which the original amplitude data page can be obtained.

Other embodiments of the method and apparatus of the present inventionrelate to Content address based data search. In one such embodimentholographic recording is carried out at the FT plane or fractional FTplane by conventionally displaying the data page on an SLM or otheroptical encoding device operating in the amplitude mode. In the presentinvention, content addressable searching is performed by displaying thesearch data patterns on an optical encoding device (SLM) that isoperating in phase mode. Correlation matching is described, for example,in B. J. Goertzen and P. A. Mitkas, Opt. Engineering, Vol 35, No. 7, pp.1847-1853 (1995) and G. W. Burr, S. Kobras, H. Hanssen, and H. Coufal,Appl. Optics, Vol. 38, No. 32, pp. 6779-6784 (1999) and G. W. Burr,SPIE, Vol. 5181, pp 70-84 (2003). In one embodiment, correlationmatching comprises the steps of displaying a search pattern on the SLMin phase mode, relaying with a lens element an object beam comprisingthe phase search pattern to one or more recorded data page holograms ina storage location in the holographic recording medium and therebyilluminating the recorded holograms with said search object beam, anddetecting a reconstructed diffracted reference beam from one or moredata page holograms containing content of the search pattern, whereinthe amount the amount of power in a diffracted reference beam isproportional to the degree of correlation between the input searchpattern and the associated data page hologram. Advantageously, theinventive method of searching allows correlation matching when the sizeof the contiguous region of matched pixels is reduced from a fullymatched data page to a smaller grouping of matched pixels. In thisembodiment correlation matching can also be achieved for the case whenthe matched pixels in the search pattern are translated or rotated fromtheir original location in either x or y directions. The amount of suchtranslation or rotation of the search pattern depends on parameters suchas thickness of the recording material, Bragg selectivity, multiplexingmethod, etc. and those experienced in the art will be able to determineappropriate conditions.

Another embodiment of the method and apparatus of the present inventionalso relates to Content address based data search. In this embodimentholographic recording is done at FT or fractional FT plane by displayingthe data page on an SLM or other optical encoding device operatingsubstantially in the phase mode, and content addressable searching isperformed by displaying the selected search data pages or patterns onsaid optical encoding device that is also operating in phase mode andpropagating the pattern in phase mode to the storage locations. In saidembodiment, correlation matching can be readily and advantageouslyachieved when the size of the contiguous region of matched pixels isdiminished from a fully matched data page to a smaller grouping ofmatched pixels that corresponds to less than about 50% of the total datapage, more advantageously correlation matching can also be achieved whenthe area of said smaller grouping of matched pixels corresponds to lessthan about 10% of the total data page, and even more advantageouslycorrelation matching can be achieved when the area of said smallergrouping of matched pixels corresponds to less than about 5% of thetotal data page. In said embodiment correlation matching can also beachieved for the case when the matched pixels in the search pattern havebeen translated or rotated from their original location in either x or ydirections. The amount of such translation or rotation of the searchpattern depends on parameters such as thickness of the recordingmaterial, Bragg selectivity, multiplexing method, etc. and thoseexperienced in the art will be able to determine appropriate conditions.

Another embodiment of the method and apparatus of the present inventionrelates to Content address based data search as well as the manner inwhich hologram are multiplexed so as to achieve advantageously highareal density for stored information, high data rates, and high searchrates. Information can be advantageously stored at high areal density inthin media so as to substantially mitigate geometric constraints thatare encountered when the Reference beam is incident at an oblique angle.

Referring to FIG. 13, the detected signal strength of the reconstructedobject beam of a recorded hologram (I) varies with either the wavelengthλ of the reference beam used to reconstruct the hologram, or angle φbetween such a reference beam and the optical axis of the object beam,said axis in this example being normal to the surface of the holographicrecording medium according to the function depicted in FIG. 13. Thecurve shown in FIG. 13 is referred to as a Bragg selectivity (in thisexample angular or wavelength) or detuning curve for address-basedretrieval. As shown in FIG. 13, the highest signal strength of thedetected hologram is achieved at wavelength λ₀ or angle φ₀ thatcorrespond to the position of the primary or principal diffraction peak(I₀). The first subsidiary maximum (having intensity I₁) is separatedfrom the primary diffraction by the 1^(st) null or minimum and isseparated from the second subsidiary maximum by the 2^(nd) null orminimum. In one embodiment of the present invention, the an anglebetween reference beams used to record two or more multiplexed hologramsis less than angular separation between a primary diffraction peak andthe 1^(st) null of a holographic angle selectivity curve. In anotherembodiment, a difference in wavelength between reference beams used torecord the multiplexed holograms is less than wave length separationbetween a primary diffraction peak and the 1^(st) null of a holographicwavelength selectivity curve. In still another embodiment, a differencein position used to record shift multiplexed holograms is less than theincrement of position between a primary diffraction peak and the 1stnull of a holographic shift selectivity curve.

In accordance with the present invention, the holograms are multiplexedco-locationally or substantially overlapped in a manner such that theangular or wavelength or positional increments for recording and/orrecovering information from said holograms correspond to less than therespective increment between the primary diffraction peak and the firstnull or minima of the corresponding Bragg selectivity curve. Hologramsrecorded in this manner can be readily differentiated during contentaddressable search, described above, when the optical encoding device(SLM) is operable in phase mode. Preferably, said increment issignificantly less than the increment between the primary diffractionpeak and the first null of the Bragg selectivity curve, such as ⅕^(th)to about 1/25^(th) of the increment so as to provide for increasing themultiplexing factor (i.e. number of co-locationally multiplexedholograms or overlapped multiplexed holograms recorded across thediameter of one storage location) by at least a value of about 5 to 25.This improvement is at least comparable to the improved multiplexingfactor that can otherwise be achieved by combining multiplexing methods,such as planar-angle and azimuthal or shift in tangential and shift inradial directions, but advantageously the opto-mechanical system forrecording and/or reading would be simplified by comparison to what isrequired when combining multiplexing methods.

By way of example, for conventional planar-angle multiplexing of digitaldata pages an increment in angle of the reference beam for multiplexingis typically equal to the increment in angle between the primarydiffraction peak and the second null or minima of the Bragg selectivitycurve (see FIG. 13) so as to provide for reasonably good SNR. When asearch of stored information is carried out with the SLM operable inphase mode, then this increment can be substantially reduced by a factorof 10 to 20 or more during recording of the multiplexed holograms, withlimitations, by way of example, being the NA of the lens that may beused to redirect the ensemble of reference beams generated by themultiplexed holograms to a digital detector, the size and number of thedetectors which by way of example can be photo diodes or CMOS detectors,distance between the detector(s) and the media, etc. A related aspect ofthis invention is that the areal density of the holographically recordedinformation can be increased substantially as compared to conventionalmethods and thereby advantageously provides for substantially highercapacity per unit thickness of the recording media, higher data rates,and higher speed data search. Another related aspect of the presentinvention is that the requirements for BER and SNR exhibited by themultiplexed holograms can be relaxed without compromising the operationof content addressable searching, and consequently the overheadassociated with encoding the data with modulation codes and errorcorrection codes can be reduced. The present invention provides forrecording on the order of a terabytes of information in the form factorof a DVD and with a thin recording material that has a thickness of onlyabout 400 microns. By the method of the present invention, raw opticalsearch rates with disk media rotating, by way of example, at 1000 rpmcan be on the order of at least about 100 Gbytes/sec.

EXEMPLIFICATION EXAMPLE 1 RECODRING A HOMOGENIZED PHASE-ENCODED DATAPAGE AND READING THE RECORDED HOLOGRAM USING EDGE ENHANCEDRECONSTRUCTION WITH 4× AND 8× OVERSAMPLING AT DETECTOR

Recording was carried out using a Coherent 315M DPSS laser emitting at532 nm. A classical 4f optical configuration was implemented usingspatially filtered coherent reference and signal beams and conventionaldoublets (f=70 mm) for all optics. Matched power densities wereimplemented for the signal and reference beams at the recording planefor recording carried out with a Displaytech ferroelectric LCD SLM(1280×768 pixels) in 0-pi phase mask conditions at Fourier Transformplane. The SLM can be operated in binary amplitude (0 and 1) as well asbinary phase (0 and π) modes by rotation of the SLM by 22.5 degrees.Alternatively, amplitude and phase mode operations of the SLM wereachieved by rotating a half-wave plate kept in front of it. During thebinary phase mode operation the Displaytech SLM, in conjunction with thepolarizing beam splitter in front of it, imparts −π/2 and +π/2 phaseshifts on the light reflected from the pixels. A Photobit MV02 CMOScamera (512×512 pixels, 16 μm pixel pitch) was used as the detectordevice. Aprilis CROP photopolymer material of 50 μm to 400 μm thicknesswas used as the holographic recording medium.

A balanced (i.e. having a substantially equal number of the opaque andtransparent pixels) 6-8 modulation coded binary data page comprisingregularly spaced fiducial markings was displayed on the SLM. FIG. 9( a)shows a part of said data page with said pixel grouping for an exampleof said fiducial marking. FIG. 9( b) shows the Fourier power spectrum ascaptured by the CMOS camera when it was positioned at the FT plane, forthe case when the SLM is operated in the amplitude mode. The presence ofthe high intensity dc peak at the center, as seen in FIG. 9( b)typically requires that the recording take place at a plane that iseither in front of or is behind the exact FT plane, or some other beamconditioning technique may be employed. FIG. 9( c) shows the Fourierpower spectrum as captured by the CMOS camera when it was positioned atthe FT plane, for the case when the SLM is operated in the 0-π phasemode. FIG. 9( c) shows that the high intensity dc peak is substantiallyabsent, due to the destructive interference between the light from 0 andπ pixels of the SLM when a balanced binary data page is presented tosaid SLM.

After displaying the data page on said SLM operating in phase mode, ahologram is recorded in the photopolymer material which is positioned atthe FT plane. When the hologram is read-out in the conventional mannerby the reference beam, with the object arm being blocked, the resultantreconstruction is the phase data page. The dc peak, however, was absentat the FT plane, as holographic recording occurred only for the accomponents of the Fourier spectrum. The resultant reconstruction is thusan edge enhanced reconstruction of the data page exhibiting the phasetransitions, as shown in FIGS. 10( a) and 10(b) for the case of 4×4 and8×8 over sampling, respectively, on the binary data page presented tothe SLM. If the value of “0” or “1” is known for any specific pixellocation in the reconstructed data page, such as would be the case forknown fiducial markings, then by edge detection means every pixel can beassigned to a “0” or “1” and, accordingly, the original data page can bereconstructed.

EXAMPLE 2 RECONSTRUCTION OF AN AMPLITUDE DATA PAGE BY INTERFERENCE OFTHE RECONSTRUCTED PHASE-MODULATED DATA PAGE AND AN IMAGED UNIFORM PAGEDISPLAYED ON THE SLM

When the phase hologram is recorded as in Example (1) thenreconstruction of the original amplitude data page from the phase imageis accomplished by using a real-time holographic interferometric method.In one embodiment, a blank (uniform) page is displayed on the phase SLM.With the object beam being kept ‘ON’, the data page hologram wasread-out by concurrent illumination with the reference beam using thecorrect reference beam angle for said data page hologram. As shown inFIG. 8, interference between the holographically reconstructed data pageand the blank (uniform) page from the SLM reproduces the original datapage, shown in FIG. 11( a), in amplitude mode for detection by the CMOScamera. The recovered data page as captured by said CMOS camera ofExample (1) is shown in FIG. 11( b). FIG. 11( c) shows the phase imageas captured directly by said CMOS camera without the recording materialat the FT plane.

EXAMPLE 3 RECONSTRUCTION OF AN AMPLITUDE DATA PAGE BY INTERFERENCE OFTHE RECONSTRUCTED PHASE-MODULATED DATA PAGE AND A BLANK CO-LOCATIONALLYRECORDED PAGE

When the phase hologram is recorded so as to use the method of Doubleexposure holographic interferometry for data recovery, a blank data page(i.e. full field super pixel), in addition to the recording of the phasedata page, was carried out near the FT plane. Upon reconstruction withthe Reference beam, the presence of the blank page hologram incombination with the phase page hologram provided for an interference ofthe two resultant diffraction wavefronts thereby providing forreconstruction of the original amplitude data page as shown in FIG. 11(d).

EXAMPLE 4 DEGREE OF CORRELATION MATCHING FOR SEARCH PATTERN HAVING 100%Of THE AREA OF THE DATA PAGE VERSUS 0% OF THE AREA OF THE DATA PAGE FORMULTIPLEXED DATA PAGE FT AND FRACTIONAL FT HOLOGRAMS RECORDED IN BINARYVERSUS AMPLITUDE MODE WITH HIGH AND LOW MODULATION DEPTH

The extent of correlation matching was evaluated for holograms recordedwith several different types of recording conditions. The ratio of theintensity of the Reference beam reconstruction was determined when usinga fully matched data page presented to the SLM versus 15 differentnon-matched data pages that were similarly presented to said SLM. Eachof the 15 different non-matched data pages comprised a balanced randomdistribution of (1s) and (0s) to simulate a standard data page. Poorcorrelation matching was achieved and significant cross correlation wasexhibited when one data page was recorded with the Displaytech SLMoperated in amplitude mode and with the recording material positioned ata distance of about 10% behind the Fourier Transform plane. Whenmultiple (15 to 30) amplitude data pages were multiplexed with planarangle multiplexing at the Fourier Transform plane then good correlationmatching was exhibited and cross correlation was nominal.

In case (i) FT plane recording of a data page was carried out with saidDisplaytech LCD SLM operating in 0-π phase conditions using the setup ofExample (1), and the recording material (400 microns thick Aprilis CROPphotopolymerizable material) was positioned at the Fourier Transformplane. The incident power densities of the reference and signal beamswere matched at the recording plane.

In case (ii) FT plane recording of a data page was carried out with saidDisplaytech LCD SLM operating in amplitude mode using the setup ofExample (1), and the recording material (400 microns thick Aprilis CROPphotopolymerizable material) was positioned at the Fourier Transformplane. The incident power densities of the reference and dc portion ofthe signal beams were matched at the recording plane.

In case (iii) FT plane recording of a data page was carried out withsaid Displaytech LCD SLM operating in amplitude mode using the setup ofExample (1), and the recording material (400 microns thick Aprilis CROPphotopolymerizable material) was positioned at the Fourier Transformplane. The incident power densities of the reference and signal beamswere mismatched at the recording plane such that I_(Ref)/I_(ACmax)=1where I_(AC) is the intensity distribution of the ac components of theFT of the object beam. Accordingly, high modulation depth was achievedfor holographic recording of the ac components, and low modulation depthfor the DC component. This approach is opposite to the conventionalmethod where the intensity of the Reference beam is typically muchgreater than I_(AC) in order to achieve good fidelity for the recordeddata page.

In case (iv) fractional FT plane recording of a data page was carriedout with said Displaytech LCD SLM operating in amplitude mode using thesetup of Example (1), and the recording material (400 microns thickAprilis CROP photopolymerizable material) was positioned at a distanceequal to about 10% of the focal distance behind the Fourier Transformplane. The incident power densities of the reference and the average ofthe signal beams were approximately matched at the recording plane.

In case (v) fractional FT plane recording of a data page was carried outwith said Displaytech LCD SLM operating in 0-π phase mode using thesetup of Example (1), and the recording material (400 microns thickAprilis CROP photopolymerizable material) was positioned at a distanceequal to about 10% of the focal distance behind the Fourier Transformplane. The incident power densities of the reference and signal beamswere matched at the recording plane.

Results for the ratio of the intensity of the Reference beamreconstruction using the matched data page at the SLM versus 15different non matched data pages comprising a balanced randomdistribution of (1s) and (0s) were as follows.

Case (i)

Intensity ratio=(80-82)/(2.1-2.5) where correlation with each of the 15non matched data pages results in a small variation in the dc signalstrength but in each case the dc level is substantially diminishedrelative to the value achieved for the matched data page. This ratioshould only be limited by diffraction efficiency of the recorded datapage. By way of example, for larger diffraction efficiency a ratio of148/0.5 was achieved.

Case (ii)

Intensity ratio=(62)/(60) where correlation with each of the 15non-matched data pages results in a small variation in the dc signalstrength but in each case the dc level is substantially similar to thevalue achieved for the matched data page.

Case (iii)

Intensity ratio=(53)/(5.35) where correlation with each of the 15non-matched data pages results in a small variation in the dc signalstrength but in each case the dc level is moderately diminished relativeto the value achieved for the matched data page.

Case (iv)

Intensity ratio=(97)/(20-22) where correlation with each of the 15non-matched data pages results in a small variation in the dc signalstrength but in each case the dc level is moderately diminished relativeto the value achieved for the matched data page.

Case (v)

Using 0-pi phase and a shift of the media position to 10% of focallength behind FT plane; Intensity ratio=(60)/(0.9-1.1) where correlationwith each of the 15 non-matched data pages results in a small variationin the dc signal strength but in each case the dc level is againsubstantially diminished relative to the value achieved for the matcheddata page.

EXAMPLE 5 CORRELATION SIGNAL STRENGTH RELATES TO CONTIGUOUS AREA FORSEARCH PATTERN RELATIVE TO 100% OF THE AREA OF A DATA PAGE

The size of the contiguous region of matched pixels of the data page ina content addressable search correlates with the magnitude of theintensity ratio of the correlation for the case when the total number ofmatched pixels is kept constant for case (i) of Example 4. For example,when the contiguous region of matched pixels is 50% of the width of thewhole data page and along the entire length of the data page (i.e. 50%of the area is matched from left to right), independent of where the 50%matched portion is positioned horizontally along the full data page,then the intensity ratio of the correlation is diminished from 56/1.2observed for a fully matched data page to 25/1.2. When the contiguousregion of matched pixels that is equal to 50% of the width of the entiredata page, however, is split into two regions oriented along the entirelength of two opposing edges of the data page, and these are separatedby a center region of random pixels extending along the entire lengthand equal to about 50% of the total pixels of the data page, then theintensity ratio of correlation is diminished further to a value slightlylarger than when 25% of the data page is matched in a contiguous region.

EXAMPLE 6 IMPROVED DISCRIMINATION FOR PHASE CONTENT SEARCH OF BALANCEDCO-LOCATIONAL BINARY AMPLITUDE DATA PAGES, MULTIPLEXED WITH ANGLEINCREMENTS LESS THAN THE ANGLE DIFFERENCE BETWEEN THE PRIMARYDIFFRACTION PEAK AND FIRST MINIMA, COMPARED TO AMPLITUDE SEARCH OFBALANCED CO-LOCATIONAL BINARY AMPLITUDE DATA PAGES

The effect of the size of the contiguous region of matched pixels of thedata page in a content addressable search was additionally examined forthe case of having recorded multiplexed amplitude data pages where eachpage was a balanced random encoded binary page and multiplexing wascarried out at less than Bragg selectivity conditions for both amplitudeand phase recording. Thirty (30) 262 kbit substantially phase data pageswere multiplexed co-locationally using planar angle multiplexing with anangle increment of the Reference beam that was reduced to about ⅕ of thefull width half height of the Bragg detuning curve, corresponding to 10times denser than with conventional planar-angle multiplexing. Inanother location, thirty (30) 262 kbit amplitude data pages weremultiplexed co-locationally using planar angle multiplexing with anangle increment of the Reference beam that was reduced to about ⅓ of thefull width half height of the Bragg detuning curve, corresponding to 6times denser than with conventional planar-angle multiplexing. Theholograms were recorded using the optical configuration of FIG. 2, asdescribed in Example (1), and exposure times were scheduled to achievesimilar diffraction efficiency for each multiplexed data page. Contentaddressable searching of the co-locational amplitude data pages wasimplemented firstly with the search pattern presented to the SLM insubstantially phase mode for the case when the angle increment wasreduced to provide for a factor of 10 times the conventional density,and, secondly, in amplitude mode for the case when the angle incrementwas reduced to provide for a factor of 6 times the conventional density.The search pattern for FIG. 12( a) corresponded to a blank pagepresented to the SLM operating in phase mode. The entire ensemble ofreconstructed Reference beams is exhibited for the 30 multiplexedholograms that were recorded at 10 times conventional density, due tothe residual dc component that was present as a consequence of the SLMnot being operated fully in phase mode. The search pattern for 8(b) wasin amplitude mode and corresponded to one fully matched page out of the30 that were co-locationally multiplexed in amplitude mode. FIG. 12( b)shows substantial cross correlation and nominal differentiation in theintensity of the reconstructed Reference beams. Thirdly, contentaddressable searching of the co-locational amplitude data pages wasimplemented with the search pattern presented to the SLM in phase mode.The search pattern again corresponded to one fully matched page out ofthe 30 that were co-locationally multiplexed. FIG. 12( c) showsnegligible evidence of cross correlation and correct identification ofthe Reference beam corresponding to the data page of the matched searchdata. Additionally, content addressable searching of the co-locationalamplitude data pages was implemented with the search pattern presentedto the SLM in phase mode, but with the search data being reduced to 75%,50%, and 25% of the fully matched data page for one of theco-locationally multiplexed data pages. FIGS. 12( d), 12(e) and 12(f)show correlation matching for the 75%, 50%, and 25% cases, respectively,and also exhibit negligible evidence of cross correlation.

EXAMPLE 7 DEGREE OF CORRELATION MATCHING FOR MULTIPLEXED PHASE DATA PAGEWHEN THE AREA OF THE CONTIGUOUS SEARCH PATTERN IS VARIED BETWEEN 100%And ABOUT 5% OF THE AREA OF THE DATA PAGE

The degree of correlation matching was determined for a phase data pagerecorded with conditions of case (i) of Example (3) when the contiguousgrouping of matched pixels used for a content addressable search by themethod of Example (3) was varied between about 5.45% and 100% of thetotal data page area.

When about 30×550 out of 550² pixels (i.e. 5.45%) of original area ofthe page is matched in a contiguous region, and the remaining ˜94.5% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, the intensity ratio of thecorrelation declined to a value of about 3/1.2, as compared to 56/1.2for a fully matched area.

When about 60×550 out of 550² pixels (i.e. 10.9%) of original area ofthe page is matched in a contiguous region, and the remaining ˜89% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, the intensity ratio of thecorrelation declined to a value of about 6.8/1.2, as compared to 56/1.2for a fully matched area.

When about 120×550 out of 550² pixels (i.e. 21.8%) of original area ofthe page is matched in a contiguous region, and the remaining ˜78% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, the intensity ratio of thecorrelation declined to a value of about 16/1.2, as compared to 56/1.2for a fully matched area.

When about 50% of original area of the page (i.e. 225×550 pixels in bothdirections) is matched in a contiguous region, and the remaining 50% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, then the intensity ratio ofthe correlation decreased from the fully matched value of 56/1.2 to25/1.2.

When about 320×550 out of 550² pixels (i.e. 58.2%) of original area ofthe page is matched in a contiguous region, and the remaining ˜42% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, the intensity ratio of thecorrelation declined to a value of about 40/1.2, as compared to 56/1.2for a fully matched area.

When about 420×550 out of 550² pixels (i.e. 76.4%) of original area ofthe page is matched in a contiguous region, and the remaining ˜23.6% ofthe page is unmatched and is, additionally, randomly distributedmaintaining the balanced modulation code, the intensity ratio of thecorrelation declined to a value of about 49/1.2, as compared to 56/1.2for a fully matched area.

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

1. A method of recording multiplexed holograms, comprising: recording a first phase-encoded Fourier transform hologram or a fractional Fourier transform hologram with a first reference beam; and recording a second phase-encoded Fourier transform hologram or a fractional Fourier transform hologram with a second reference beam at the same location or at a substantially overlapped location on a holographic recording medium, wherein the angle between the first and the second reference beams is less than the angular separation between the primary diffraction peak and the first minimum of the Bragg angle selectivity curve of the first or the second holograms.
 2. The method of claim 1, wherein the angular separation of the first and the second reference beam is less than about 1/10 of the angular separation between the primary diffraction peak and the first minimum of the Bragg angle selectivity curve of the first or the second holograms.
 3. A method of recording multiplexed holograms, comprising: recording a first phase-encoded Fourier transform hologram or a fractional Fourier transform hologram with a first wavelength; and recording a second phase-encoded Fourier transform hologram or a fractional Fourier transform hologram with a second wavelength at the same location or at a substantially overlapped location on a holographic recording medium wherein the difference between the first and the second wavelengths is less than the wavelength separation between the primary diffraction peak and the first minimum of the Bragg wavelength selectivity curve of the first or the second holograms.
 4. The method of claim 3, wherein the wavelength separation of the first and the second holograms is less than about 1/10 of the wavelength separation between the primary diffraction peak and the first null of the Bragg wavelength selectivity curve of the first or the second holograms.
 5. A method of recording multiplexed holograms, comprising: recording a first Fourier transform hologram or a fractional Fourier transform hologram with a first reference beam; and recording a second Fourier transform hologram or a fractional Fourier transform hologram with a second reference beam at the same location or at a substantially overlapped location on a holographic recording medium, wherein either the difference in angle or the difference in wavelengths between the first and second reference beams is less than either the angular separation or wavelength separation, respectively, between the primary diffraction peak and the first minimum of a Bragg selectivity curve of the first or the second holograms.
 6. The method of claim 5, wherein the angle between the first and second reference beams is less than the angular separation between the primary diffraction peak and the first minimum of the Bragg angle selectivity curve of the first or the second hologram.
 7. The method of claim 6, wherein the angular separation of the first and second reference beam is less than about ¼th of the angular separation between the primary diffraction peak and the first minimum of the Bragg angle selectivity curve of the first or the second hologram.
 8. The method of claim 6 wherein the recorded multiplexed holograms are phase encoded data pages.
 9. The method of claim 6, wherein the angular separation of the first and second reference beam is less than about 1/10th of the angular separation between the primary diffraction peak and the first minimum of the Bragg angle selectivity curve of the first or the second hologram.
 10. The method of claim 5, wherein the first and second reference beams are at first and second wavelengths, respectively, and wherein the wavelength difference between the first and second wavelengths is less than the wavelength separation between the primary diffraction peak and the first minimum of the Bragg wavelength selectivity curve of the first or the second hologram.
 11. The method of claim 10 wherein the recorded multiplexed holograms are phase encoded data pages.
 12. The method of claim 10, wherein the wavelength separation of the first and second hologram is less than about ¼th of the wavelength difference between the primary diffraction peak and the first minimum of the Bragg wavelength selectivity curve of the first or the second hologram.
 13. The method of claim 10, wherein the wavelength separation of the first and second hologram is less than about 1/10th of the wavelength difference between the primary diffraction peak and the first minimum of the Bragg wavelength selectivity curve of the first or the second hologram. 